§1.1 Field of the Invention
The present invention concerns detecting the presence of, and/or measuring the amount or concentration of substances, such as chemical and/or biological substances for example. More specifically, the present invention concerns detecting and/or measuring a substance based on a resonance shift of photons orbiting within a microsphere.
§1.2 Related Art—Measurement Principle Using Ray Optics in Microsphere Having a Changing Size
Resonances in a geometrical optics limit are associated with the optical ray paths, such as those 110 illustrated in the cross section of a particle 100 illustrated in FIG. 1. Total internal reflection keeps the photon(s) from radiating outward. Collectively, the ray path segments 110 define a polygon.
Basically, the light circles (or orbits) the interior of the particle 100, returning in phase. This is known as a mode of the first order. For higher order modes, the photon(s) takes several orbits before its ray path closes—i.e., before the photon returns in phase.
The foregoing illustration and assumptions are appropriate for meso-optic elements (i.e., devices, comparable in size to the wavelength of light, that can confine photons) 100 having a diameter 2a that is between 10 and 100 times the wavelength of the photon. The resonances have specific polarization states.
Referring to FIG. 2, an optical fiber 200 may be evanescently coupled with a microsphere 100′. More specifically, an evanescent electromagnetic field associated with total internal reflection exists just outside the microsphere 100′, decaying exponentially as a function of distance, typically over a distance of ˜0.1 μm. Further, internal reflection on a curved surface induces a small amount of radiation leakage in the far field. The higher the order of the mode, the greater the leakage. For example, the energy loss in one oscillation within slightly spheroidal fused silica microspheres (2a>˜50 μm) has been measured to be smaller than 2 billionths of the energy contained, yielding a quality factor Q>˜108. Stated in another way, the linewidth of the associated resonance (δf) in the spectrum is 10 billionth of the frequency (δf=f/Q). Referring to FIG. 3, the resonance modes can be detected as transmission dips 300 in the evanescently coupled optical fiber 200.
As illustrated in FIG. 4, if the size (or shape, or refractive index) of the particle 100/100′ changes, the resonances shift in frequency. For example, in the case of a sphere, as its radius increases, the resonance occurs at a longer wavelength. This shift can be expressed as:
                                          Δ            ⁢                                                  ⁢            a                    a                =                  Δλ          λ                                    (        1        )            
This relationship may be derived as follows.
When considering size sensitivity, recognize that the angular momentum L of the photon in a given mode is quantized. That is
      L    =                  (                  h                      2            ⁢            π                          )            ⁢                        l          ⁡                      (                          l              +              1                        )                                ,where l is an integer and h is Plank's constant. The angular momentum in the geometry of FIG. 1 is equal to its linear momentum (p) times the distance of the closest approach from the sphere center (a cos(π/q)), where q is the number of reflections in the orbit. The linear momentum p of the photon is its energy (hf) divided by the speed of light in the medium. That is, p=hfn/c, where f is the frequency, n is the refractive index of the sphere, and c is the speed of light in vacuum. Consequently, the angular momentum may be expressed as:
                    L        =                                            hfna              c                        ⁢            cos            ⁢                          π              q                                =                                    hna              λ                        ⁢            cos            ⁢                                                  ⁢                          π              q                                                          (        2        )            where λ is the wavelength in vacuum.
Since the resonance mode has a constant angular momentum, equation (2) can be used to estimate the effect that various perturbations have on the resonance wavelength. For example, to reiterate, as was illustrated in FIG. 4, if the size (or shape, or refractive index) of the particle 100/100′ changes, the resonances shift in frequency. In the case of a sphere, as its radius increases, the resonance occurs at a longer wavelength. This shift can be expressed as:
                                          Δ            ⁢                                                  ⁢            a                    a                =                              Δ            ⁢                                                  ⁢            λ                    λ                                    (        1        )            
The sensitivity of this measurement technique can be estimated as follows. If it is assumed that the linewidth (δλ≅10−8λ), then the smallest “measurable” size change is |Δa|min=10−8a. Assuming a sphere radius (a) on the order of 10 μm, |Δa|min=1013 m. This is much smaller than the size of an atom.
Unfortunately, the resonance of photon(s) orbiting within a microsphere is fairly sensitive to changes in temperature. To estimate the resonance shift due to temperature change, both the radius and refractive index (n) of the microsphere are permitted to vary. Based on equation (2), the fractional shift in wavelength may be expressed as:
                              Δλ          λ                =                                            Δ              ⁢                                                          ⁢              a                        a                    +                                    Δ              ⁢                                                          ⁢              n                        n                                              (        3        )            
In most amorphous optical materials, both the size and the refractive index will change approximately linearly with temperature at near room temperature. Thus, there is a need for improving the foregoing technique of detecting and/or measuring a substance based on a resonance shift of photons orbiting within a microsphere, by making it insensitive or less sensitive to changes in temperature. Indeed, it would be useful to make the foregoing technique insensitive or less sensitive to changes other than changes in the amount or concentration of the substance being detected or measured.
Other challenges to using the foregoing technique include (i) connecting the microsphere to the optical fiber to ensure adequate mechanical reliability and adequate optical coupling, and (ii) attaching receptors to the microsphere.